Help about ratio and proportion

The ratio between the incomes of two people is 5:3. The ratio between their expenditures is 8:5, while the ratio between their savings is 4:3. What will be the ratio between their combined Incomes and Combined Expenditures. (Answer = 32:39) Please tell me how to do it.

This is 3 equations in 4 unknowns, so we can choose one of the values. I will set

Now:

You should be able to solve that system of simultaneous equations to get

The ratio you want is

Its interesting to note that the savings amount comes out as negative for both people...but thats another story.

If you are interested in why i can set without breaking the answer, its because we are only interested in ratios, not the actual levels of income. I am effectively redefining the currency unit of the problem so that has 1 unit.

The ratio between the incomes of two people is 5:3. The ratio between their expenditures is 8:5, while the ratio between their savings is 4:3. What will be the ratio between their combined Incomes and Combined Expenditures. (Answer = 32:39) Please tell me how to do it.